EEG and MEG are common techniques for measuring, at the surface of the head, electric and magnetic field potentials generated by operation of the brain. An array of sensors, typically electrodes in the case of EEG, and SQUID sensors in the case of MEG, is provided, the sensors being distributed over the head surface.
There is an understanding in the art regarding the number of sensors needed to accurately record the electrical or magnetic field potentials produced by brain activity, and 64 sensors is recognized as being insufficient. The understanding derives from the Nyquist theorem, which is often used to define the minimum temporal sampling rate for sampling a continuous signal based on the highest frequency (Fourier) component of the signal. According to the Nyquist theorem, to fully code and therefore fully define a continuous signal having a highest frequency component of frequency X, the signal must be sampled at a sampling rate of 2X. In practice, the signal is sampled at a higher rate, typically about 2.5 X, to account for the non-stepwise response of real filters, i.e., real filters “roll off” over a frequency range.
The Nyquist theorem has been extended in the present art to define spatial frequencies, i.e. the number of cycles of a signal, or a Fourier component thereof, per unit distance (e.g., X is expressed in cycles/cm). Thus, there is a theoretical minimum Nyquist sampling rate (theoretical maximum spacing between sensors) of ½·X−1, where X−1 is the spatial period.
As in the time domain, there is a corresponding practical minimum spacing of about 1/(2.5)·X−1, corresponding to a higher sensor density. The difference is 0.10·X−1 or 25%, and is referred to as “spatial oversampling.” Spatial oversampling, like time oversampling, is provided for the purpose of complying with the Nyquist theorem in practice, to ensure that the signal is in fact fully and faithfully characterized by the data.
Spatial oversampling has been used in academic research, such as exemplified by Walter J. Freeman et al. (“Spatial spectra of scalp EEG and EMG from awake humans,” Elsevier Clinical Neurophysiology 114 (2003) 1053-1068). But spatial oversampling is typically not utilized in commercial practice, as it leads to higher cost and complete accuracy has not been considered essential.